US10088825B2 - Tool path curve generation method and tool path curve generation apparatus - Google Patents

Tool path curve generation method and tool path curve generation apparatus Download PDF

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US10088825B2
US10088825B2 US14/952,904 US201514952904A US10088825B2 US 10088825 B2 US10088825 B2 US 10088825B2 US 201514952904 A US201514952904 A US 201514952904A US 10088825 B2 US10088825 B2 US 10088825B2
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curve
region
tool path
point sequence
points
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US20160154400A1 (en
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Tohru Mizuno
Takuji Chiba
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Fanuc Corp
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Fanuc Corp
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G05B19/27—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path using an absolute digital measuring device
    • G05B19/31—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path using an absolute digital measuring device for continuous-path control
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B15/00—Systems controlled by a computer
    • G05B15/02—Systems controlled by a computer electric
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
    • G05B19/4103—Digital interpolation
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/50—Machine tool, machine tool null till machine tool work handling
    • G05B2219/50336—Tool, probe offset for curves, surfaces, contouring

Definitions

  • the present invention relates to a tool path curve generation method and a tool path curve generation apparatus that ensure a shape error of a predetermined value or less.
  • the curves generated from divided groups of points are expressed in the form of parametric curves.
  • An expression form such as a B-spline curve or a NURBS curve, which is suited for each application, is adopted.
  • a curve generated from a point sequence provides a smooth path
  • the curve is required to pass by an original point sequence. For this reason, according to a conventional method for creating curves, a curve is generated such that the distance between each point of a point sequence and a point corresponding thereto on the curve will take a preset value or less.
  • Japanese Patent Application Laid-Open No. H10-240329 describes a method in which, in the case of an interpolation curve, some points are taken on a curve sandwiched between command points, and the distance between a segment that connects the command points and each of the points is observed. This method allows more detailed determination than the method in which the distance is observed only at command points. However, the section sandwiched between adjacent points is not checked, thus failing in principle to ensure that an error is an allowable value or less.
  • the present invention has been made to solve the foregoing problem with the generation of curves according to the prior arts, and it is an object of the invention to provide a tool path curve generation method and a tool path curve generation apparatus which ensure a shape error such that an entire generated curve lies within a predetermined region as observed from an original point sequence.
  • the present invention provides a method for generating curves from a tool path drawn in the form of a point sequence.
  • a curve is generated such that a shape error between a generated curve and an original path becomes a specified value or less.
  • a conventional method for generating a curve is used. More specifically, a control point, which is a variable for changing the shape of a curve is introduced, and the position of the control point is determined such that the sum of the distances between the curve and each point of a point sequence is minimized.
  • the method for expressing the curve having the control point as a variable and for determining the control point adopts the technique for determining an approximated curve described in “Les Piegl, Wayne Tiller, The NURBS Book, Springer-Verlag, pp 405-453.”
  • the distance between a command point and the curve is determined. Then, the control point is repeatedly added to generate the curve and the distance between the added control points and the curve is repeatedly checked until the distances of all control points become the specified value or less. If all the command points lie within a specified distance from the curve, then it is determined whether the generated curve is included in a space region based on a polygonal line path that connects the point sequence. The control points are repeatedly added to generate the curve, and the distance is repeatedly checked until the entire curve is included in the specified region, thereby obtaining a desired curve.
  • a simplest example of such a region is connected cylinders having their axes formed of individual segments constituting the polygonal line.
  • the method in accordance with the present invention is not limited to such a cylindrical region.
  • the determination unit uses only the information on a generated curve and is independent of the method itself for generating curves, enabling the determination unit to be applied regardless of the method for generating curves.
  • the tool path curve generation method in accordance with the present invention is a method for generating a curve from a tool path designated by a command point sequence, and includes: a step of defining a region based on a polygonal line path connecting the command point sequence; a step of determining whether the curve is included in the region on the basis of the geometric shape of the surface of the region; and a step of generating a curve that has been determined to be included in the region in the determination step.
  • the tool path curve generation method makes it possible to designate the shape of the region by setting.
  • the region may be a rotating body formed by rotating a curve about an axis that is a segment connecting adjacent command points.
  • a tool path curve generation apparatus in accordance with the present invention is adapted to generate a curve from a tool path designated by a command point sequence, and includes: a definition unit that defines a region based on a polygonal line path connecting the command point sequence; a determination unit that determines whether the curve is included in the region on the basis of the geometric shape of the surface of the region; and a curve generation unit that generates a curve determined to be included in the region by the determination unit.
  • the tool path curve generation apparatus allows the shape of the region to be specified by setting.
  • the region may be a rotating body formed by rotating a curve about an axis that is a segment connecting adjacent command points.
  • the present invention provided with the steps or configuration described above makes it possible to obtain a curve, the distance of which from a polygonal line path that connects the point sequence does not exceed a predetermined value.
  • the shape of the region can be specified by setting, thus making it possible to control the deviation of a curve from an original point sequence to a desired range for each machining program when generating curves of a machining path formed of the point sequence.
  • the region is made of a rotating body formed by rotating a curve about an axis that is a segment connecting adjacent command points.
  • the present invention equipped with the foregoing steps or configuration makes it possible to provide a tool path curve generation method and a tool path curve generation apparatus which ensure a shape error that causes the entire generated curve to be included in a predetermined region as observed from an original point sequence.
  • FIG. 1 is a block diagram illustrating the configuration of a tool path curve generation apparatus
  • FIG. 2 is a diagram illustrating an example of point sequence data
  • FIG. 3 is a diagram illustrating an element region constituting an allowable region
  • FIG. 4 is a flowchart illustrating the processing of generating an arc
  • FIG. 5 is a diagram illustrating the intersection points of a cylindrical element region and a curve
  • FIG. 6 is a diagram illustrating a curve section not included in the cylinders
  • FIG. 7 is a diagram illustrating a spheroid that includes the curve
  • FIG. 8 is a diagram illustrating a path that connects two points via a point on the surface of the cylinder
  • FIG. 9 is a diagram illustrating the curve of the connection part of the cylinder.
  • FIG. 10 is a flowchart illustrating the processing of verifying whether a curve section is included in the allowable region
  • FIG. 11 is a flowchart illustrating the processing of determining whether a curve section is included in the cylindrical element region.
  • FIG. 12 is a flowchart illustrating the processing of determining whether a curve section is included in a cylindrical connection region.
  • Each point sequence obtained by division to generate a curve is defined as a partial point sequence, and a curve generated from the partial point sequence will be defined as an arc.
  • a region which is defined on the basis of a polygonal line path connecting the points of a partial point sequence and in which a curve should be included so as to ensure the shape error of the curve is defined as an allowable region.
  • the allowable value of the distance between each point of the partial point sequence and the curve or the distance between a segment that connects the points of the partial point sequence and the curve is defined as a tolerance.
  • FIG. 1 is a block diagram illustrating a tool path curve generation apparatus, which is an embodiment of the present invention.
  • a tool path curve generation apparatus 1 includes an NC command decoder 10 , a point sequence acquirer 20 , a curve generator 30 , a shape error determiner 40 , and a curve output unit 50 .
  • the NC command decoder 10 is identical to an NC command decoder mounted on a numerical controller, which controls a machine tool, and decodes an NC command 2 (machining program) to extract point sequence data of a point sequence constituting a tool path.
  • the point sequence data is the data that indicates the positions of points on the tool path. In the case of five-axis machining, the point sequence data also includes the data that indicates the orientation of a tool.
  • FIG. 2 illustrates the configuration of the point sequence data for three-axis machining.
  • the data on one point is composed of the coordinates X, Y and Z of the distal end of a tool, and the same quantity of pieces of this data as the number of points is included in the point sequence data.
  • the point sequence acquirer 20 sends a request to the NC command decoder 10 to acquire necessary point sequence data. Basically, the data on the points of a predetermined number N is acquired. If there is a place determined to have a bend point of a tool path in the requested point sequence, then the point sequence data up to the bend point is acquired.
  • the curve generator 30 generates an arc.
  • the arc is a parametric curve that passes the start point and the end point of a partial point sequence and passes by the remaining points.
  • a B-spline curve is used.
  • other type of curve such as a NURBS curve or a partitioned polynomial curve, may be used.
  • the arc is represented by expression (1).
  • u denotes a parameter of the curve and takes a value in a range defined by 0 ⁇ u ⁇ 1
  • N i,3 (u) denotes a three degree B-spline basis function
  • ⁇ right arrow over (P) ⁇ i (u) denotes a control point of a B-spline curve.
  • Ensuring the shape error of a curve means to verify that the curve represented by expression (1) is included in an allowable region.
  • the allowable region is formed of connected element regions, each of which is defined for each segment constituting a polygonal line.
  • the element regions will be cylinders each having a segment as its axis and a tolerance as its radius, and a sphere that covers a cylinder connection part in which a curve is included in neither of the cylinders ( FIG. 3 ).
  • Nd denotes the number of the element regions.
  • a curve with the ensured shape error is generated as follows.
  • the values of the numbers of the knots and the control points are decided to generate a curve according to the method described in Les Piegl, Wayne Tiller, The NURBS Book, Springer-Verlag, pp 405-453, or I. J. Schoenberg, Spline functions and the problem of graduation, Proceedings of the National Academy of Sciences of the U.S.A., 52 (1964), pp 947-950), and it is verified whether the curve is included in the allowable region. Until the curve is included in the allowable region, the knots and the control points are repeatedly added to generate curves and the verification is repeatedly performed, thereby generating the curve with an ensured shape error.
  • ⁇ denotes the tolerance
  • ⁇ right arrow over (Q) ⁇ k denotes a point of the partial point sequence
  • ⁇ k denotes the value of a parameter of a point closest to ⁇ right arrow over (Q) ⁇ k on the curve
  • ⁇ right arrow over (C) ⁇ ( ⁇ k ) denotes the point.
  • Step SA 100 Set the numbers of knots and control points to initial values.
  • Step SA 101 Generate an arc.
  • Step SA 102 Whether each point of the partial point sequence lies within a tolerance from the curve is determined according to expression (3). If all points lie within the tolerance, then the procedure proceeds to step SA 103 , or if not, then the procedure proceeds to step SA 104 .
  • Step SA 103 Whether each curve element is included in its corresponding element region is determined according to expression (2). If all curve elements are included, then it means that the curve is obtained, so that the processing is terminated. If the determination result is negative, then the procedure proceeds to step SA 104 .
  • Step SA 104 The numbers of knots and control points are increased, and the procedure returns to step SA 101 .
  • a first method will be described. This method is used to verify that the maximum value of the length of a perpendicular drawn from a point P on a curve section sandwiched between Ak and Bk down to the axis of the cylinder is the tolerance or less.
  • the foot of the perpendicular is denoted by Q, and the point at which the length of PQ reaches a maximum value is determined. If the maximum value is the tolerance or less, then the curve is included in the cylinder.
  • the maximum value lies either at the end point Ak or Bk of the section or at a point at which the length of PQ takes an extreme value therebetween. Hence, the distance between each of these points and the curve is determined and a maximum value among the obtained results is adopted.
  • the position of Q is represented by expression (4), using the parameter u.
  • u k denotes the ratio of the length of the polygonal line from the start point of the partial point sequence to Qk with respect to the total length of the polygonal line (the length from the start point to the end point of the partial point sequence).
  • the relationship represented by expression (6) holds between parameters of ⁇ right arrow over (C) ⁇ (v) and ⁇ right arrow over (Q) ⁇ (u).
  • expression (7) which is a fifth degree equation related to the parameter ⁇ , determines the parameter of the point at which the length of PQ takes an extreme value.
  • the positions of P and Q are determined, and the maximal value (or the minimal value) of the length can be obtained.
  • the solution of the fifth degree equation is determined using the Newton method.
  • the codomain of the parameter is defined by 0 ⁇ u ⁇ 1, and therefore no extreme value exists in some cases. In such a case, the distance will be maximum at the end point Ak or Bk.
  • the Newton method is a well-known method, so that the description thereof will be omitted.
  • Expression (8) is a three degree equation related to ⁇ k , so that the solution thereof can be easily obtained.
  • the position of Bk is determined in the same manner.
  • the extreme values of AkQk, BkQk+1, and PQ have been determined, and the maximum value thereamong is defined as dmax (or AkQk or BkQk+1, whichever is larger, is defined as dmax if PQ does not have an extreme value).
  • Expression (10) is a fifth degree equation. As with the case of the cylinders, the Newton method is applied to obtain the solution.
  • a second determination method will now be described. This method is based on the fact that a curve having a length Lk between two points Ak and Bk is included in a spheroid having Ak and Bk as focal points and the sum of the distances from the focal points is Lk, as illustrated in FIG. 7 , and the method is used to check whether the spheroid is included in the cylinder. As with the first determination method, another determination method is applied to the cylindrical connection part, so that merely checking whether the spheroid protrudes from the side surface of the cylinder is sufficient, and the case where the spheroid protrudes from the bottom surface thereof is ignored.
  • Whether the spheroid protrudes from the side surface of the cylinder can be directly determined by projecting the spheroid and the cylinder onto a plane that is orthogonal to the axis of the cylinder. However, a simpler method described below is adopted.
  • Lk does not exceed the minimum value of the length of the polygonal line path that extends from Ak to Bk via a point P on the side surface of the cylinder. In other words, it is determined whether Lk satisfies expression (11). If Lk satisfies expression (11), then it means that the spheroid does not protrude from the side surface of the cylinder.
  • L 1 and L 2 denote the lengths of AP and PB, respectively.
  • checking whether expression (11) is satisfied makes it possible to determine whether the spheroid protrudes from the side surface of the cylinder, so that the problem to be solved comes down to determining the minimum value of L 1 +L 2 .
  • L L 1 +L 2
  • Expression (13) indicates an extreme value problem with constraint conditions and the solution can be obtained by a well-known method, such as Lagrange's method of undetermined multipliers, Goldstein, Classical Mechanics, Yoshioka Shoten (1967), pp 46-51.
  • connection part of the cylinder can be also handled as the extreme value problem with constraint conditions.
  • the following will describe the procedure.
  • Lk the length of the curve between Bk ⁇ 1 and Ak
  • the curve does not protrude from the circle if Lk does not exceed the minimum value of the length of the polygonal line that extends from Bk ⁇ 1 to Ak via a point P on the circumference.
  • the minimum value of L under the constraint conditions of expression (13) is determined.
  • the solution can be obtained by the Lagrange's method of undetermined multipliers.
  • Step SB 101 The end point Bk of the curve section and the curve length Lk from the end points Ak and Bk are determined.
  • Step SB 102 The determination is made in the case where the element region is cylindrical, as illustrated in FIG. 5 . The procedure will be described in detail later.
  • Step SB 103 If the determination result of step SB 102 indicates that the curve section is not included in the cylinder, then the procedure proceeds to step SB 109 . If the determination result indicates that the curve section is included in the cylinder, then the procedure proceeds to the determination in the connection part in step SB 104 .
  • Step SB 105 If the determination result of step SB 104 indicates that the curve section is not included in the connection part, then the procedure proceeds to step SB 109 . If the determination result indicates that the curve section is included in the connection part, then the procedure proceeds to step SB 106 .
  • Step SB 106 It is determined whether the curve section is a last one. If the curve section is the last curve section, then the procedure proceeds to step SB 108 . If the curve section is not the last one, then the procedure proceeds to step SB 107 .
  • Step SB 107 The procedure increments k by 1 and proceeds to the next curve section and returns to step SB 101 .
  • Step SB 108 It is determined that the curve is included in the allowable region.
  • Step SB 109 It is determined that the curve is not included in the allowable region.
  • Step SC 102 It is determined that the curve section is included in the cylindrical region.
  • Step SC 103 It is determined that the curve section is not included in the cylindrical region.
  • Step SD 102 It is determined that the curve section is included in the region of the connection part.
  • Step SD 103 It is determined that the curve section is not included in the region of the connection part.

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JP2014242013A JP5926358B1 (ja) 2014-11-28 2014-11-28 形状誤差を保証する工具経路の曲線化方法および曲線化装置
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JP6740199B2 (ja) 2017-10-30 2020-08-12 ファナック株式会社 数値制御装置、ｃｎｃ工作機械、数値制御方法及び数値制御用プログラム
JP6646027B2 (ja) * 2017-10-30 2020-02-14 ファナック株式会社 ポストプロセッサ装置、加工プログラム生成方法、ｃｎｃ加工システム及び加工プログラム生成用プログラム
CN108170094B (zh) * 2017-12-12 2020-05-15 烟台大学 一种刀具路径平滑压缩的方法
US10838400B2 (en) * 2018-06-20 2020-11-17 Autodesk, Inc. Toolpath generation by demonstration for computer aided manufacturing
CN109884988B (zh) * 2019-02-26 2020-09-01 浙江大学 一种五轴数控制孔机床的制孔法向插补修正方法
CN116483025B (zh) * 2023-04-23 2024-03-22 赛诺威盛科技(北京)股份有限公司 飞焦点模式下的数据采集系统、方法、电子设备及介质

Citations (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0384925A1 (de) 1989-02-28 1990-09-05 Siemens Aktiengesellschaft Steuerungsverfahren bei einer numerischen Werkzeugmaschine oder einem Roboter
US5566288A (en) * 1994-09-02 1996-10-15 Caterpillar Inc. System and method for automatically fitting a B-spline curve to a set of data points
JPH09160623A (ja) 1995-12-06 1997-06-20 Toyoda Mach Works Ltd 工作物加工用数値制御装置
JPH10240329A (ja) 1997-02-26 1998-09-11 Mitsubishi Electric Corp 曲線の微小線分化方法およびスプライン補間機能を有する数値制御装置
JP2004078516A (ja) 2002-08-16 2004-03-11 Fanuc Ltd 曲線補間方法
JP2005182437A (ja) 2003-12-19 2005-07-07 Fanuc Ltd 数値制御装置及び数値制御方法
US20060247820A1 (en) 2005-05-02 2006-11-02 Fanuc Ltd Curve interpolating method
JP2007293478A (ja) 2006-04-24 2007-11-08 Fanuc Ltd 曲線補間方法
CN101109944A (zh) 2007-08-23 2008-01-23 上海交通大学 五轴数控加工光滑无干涉刀具路径的规划方法
CN101907876A (zh) 2010-05-28 2010-12-08 沈阳高精数控技术有限公司 适用于数控装置的指令点整形压缩插补方法
US20130218323A1 (en) 2012-02-20 2013-08-22 Fanuc Corporation Numerical controller with machining curve creating function

Patent Citations (16)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP0384925A1 (de) 1989-02-28 1990-09-05 Siemens Aktiengesellschaft Steuerungsverfahren bei einer numerischen Werkzeugmaschine oder einem Roboter
US5028855A (en) 1989-02-28 1991-07-02 Siemens Aktiengesellschaft Control process for a numerically controlled machine-tool or for a robot
US5566288A (en) * 1994-09-02 1996-10-15 Caterpillar Inc. System and method for automatically fitting a B-spline curve to a set of data points
JPH09160623A (ja) 1995-12-06 1997-06-20 Toyoda Mach Works Ltd 工作物加工用数値制御装置
JPH10240329A (ja) 1997-02-26 1998-09-11 Mitsubishi Electric Corp 曲線の微小線分化方法およびスプライン補間機能を有する数値制御装置
JP3366213B2 (ja) 1997-02-26 2003-01-14 三菱電機株式会社 曲線の微小線分化方法およびスプライン補間機能を有する数値制御装置
JP2004078516A (ja) 2002-08-16 2004-03-11 Fanuc Ltd 曲線補間方法
US20040122549A1 (en) * 2002-08-16 2004-06-24 Fanuc Ltd. Curve interpolation method
JP2005182437A (ja) 2003-12-19 2005-07-07 Fanuc Ltd 数値制御装置及び数値制御方法
US20060247820A1 (en) 2005-05-02 2006-11-02 Fanuc Ltd Curve interpolating method
JP2006309645A (ja) 2005-05-02 2006-11-09 Fanuc Ltd 曲線補間方法
JP2007293478A (ja) 2006-04-24 2007-11-08 Fanuc Ltd 曲線補間方法
CN101109944A (zh) 2007-08-23 2008-01-23 上海交通大学 五轴数控加工光滑无干涉刀具路径的规划方法
CN101907876A (zh) 2010-05-28 2010-12-08 沈阳高精数控技术有限公司 适用于数控装置的指令点整形压缩插补方法
US20130218323A1 (en) 2012-02-20 2013-08-22 Fanuc Corporation Numerical controller with machining curve creating function
JP2013171376A (ja) 2012-02-20 2013-09-02 Fanuc Ltd 加工曲線作成機能を有する数値制御装置

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
Goldstein, "Lagrange's Method of Undetermined Multipliers," Classical Mechanics, (1967), pp. 46-51, Addison-Wesley Publishing Company, Inc.
Office Action dated Jan. 26, 2016, in Japanese Patent Application No. 2014-242013.
Office Action in CN Application No. 201510843828.8, dated May 2, 2017.
Office Action in DE Application No. 102015120118.6, dated Feb. 5, 2018, 9 pp.
Piegl, et al., "The NURBS Book," 2nd. Ed. (Nov. 14, 1996), pp. 405-453, Springer-Verlag.
Pottmann et al., On optimal tolerancing in Computer-Aided Design, 2000, IEEE, Geometric Modeling and and Processing, pp. 347-363 (Year: 2000). *
Schoenberg, "Spline Functions and Problem of Graduation", Proceedings of the National Academy of Sciences of the U.S.A., 52 (Aug. 18, 1964), pp. 947-950.

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